Theoretical and conceptual analysis of the celebrated 4$\pi$-symmetry neutron interferometry experiments

TL;DR

This paper provides a comprehensive theoretical and conceptual analysis of the 4π-symmetry neutron interferometry experiments, clarifying the underlying physics and challenging common interpretations about wave function sign change and particle nature.

Contribution

It offers a detailed theoretical solution to the Schrödinger equation for the experiment and a conceptual reinterpretation of the neutron's phase change mechanism.

Findings

Explicit expressions for beam intensities and interference patterns.

Confirmation that 4π-symmetry arises from a longitudinal Stern-Gerlach effect.

Experiments do not demonstrate wave function sign change but suggest particles are non-spatial entities.

Abstract

In 1975, two experimental groups have independently observed the 4$\pi$-symmetry of neutrons' spin, when passing through a static magnetic field, using a three-blade interferometer made from a single perfect Si-crystal (analogous to the Mach-Zehnder interferometer of light optics). In this article, we provide a complete analysis of the experiment, both from a theoretical and conceptual point of view. Firstly, we solve the Schr\"odinger equation in the weak potential approximation, to obtain the amplitude of the refracted and forward refracted beams, produced by the passage of neutrons through one of the three plates of the LLL interferometer. Secondly, we analyze their passage through a static magnetic field region. This allows us to find explicit expressions for the intensities of the four beams exiting the interferometer, two of which will be interfering and show a typical 4$\pi$-symmetry, when the strength of the magnetic field is varied. In the last part of the article, we provide a conceptual analysis of the experiment, showing a neutron's phase change, when passing through the magnetic field, is due to a longitudinal Stern-Gerlach effect, and not to a Larmor precession. We also emphasize that these experiments do not prove the observability of the sign change of the wave function, when a neutron is 2$\pi$ rotated, but strongly indicate that the latter, like any other elementary "particle," would be a genuinely non-spatial entity.